Mathematics · Group Theory
Let G = {A = ⌈a a⌉ ⌊a a⌋ : a ∈ ℝ ∖ {0}} and the binary operation * be defined as matrix multiplication (A * B = AB). Which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1The matrix ⌈1/4 1/4⌉ ⌊1/4 1/4⌋ ∈ G is the identity element for *✓
- 2The matrix ⌈1 1⌉ ⌊1 1⌋ ∈ G is the identity element for *
- 3G contains an identity element for *, which is the standard identity matrix I2
- 4G does not contain an identity element for *
Correct answer
The matrix ⌈1/4 1/4⌉ ⌊1/4 1/4⌋ ∈ G is the identity element for *
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